Yes they’ll be fine.
The M44-7s are very popular with scratch DJs and turntablists because they track and hold the groove very well. They’re a bit hard on the vinyl tho if vinyl wear is an issue. Their M44Gs or M35Xs may be a better choice if record wear is an issue and you’re not into scratching and turntablism.
The styli need to match the carts. When you buy new carts they will come with styli, it’s a good idea to consider the price of replacement styli when buying carts tho as they will wear out or get damaged and need replacing at some point.
A cheaper alternative is to just buy new styli for the carts you have. If you picked up the Stantons 2nd hand you may just need to give the styli a good clean, if you’re lucky .